Question

Calculați (2 +4 +6+ ... + 100) - (1+3+5+...+99). ​

Answer 1

Răspuns:

=(12+12+100)-(9+9+99)=124+117=231

Answer 2

$2 + 4 + 6 + ... + 100 \\ = 2(1 + 2 + 3 + ... + 50) \\ = 2 \times \frac{50 \times (50 + 1)}{2} \\ = 50 \times 51 \\ = 2550$

$1 + 3 + 5 + ... + 99 = n {}^{2} \\ n = nr \: \: de \: \: termeni \\ \\ n = \frac{99 + 1}{2} = 50 \\ \\ n {}^{2} = 50 {}^{2} = 2500$

$2550 + 2500 = 5050$